Question

root 7 plus root 2 divide by 9 plus root 14​

Answer 1

GIVEN :-

$\dfrac{ \sqrt{7} + \sqrt{2} }{9 + \sqrt{14} }$

TO FIND:-

Rationalize the denominator

SOLUTION:-

For Rationalising the denominator We have to multiply and divide with its Rationalizing factor

Rationalizing factor is nothing but just we have to change the sign

Rationalising factor of

$\sqrt{9} + \sqrt{14} = \sqrt{9} - \sqrt{14}$

So, multiply and divide with this

$\dfrac{ \sqrt{7} + \sqrt{2} }{9 + \sqrt{14} } \times \dfrac{9 - \sqrt{14} }{9 - \sqrt{14} }$

$\dfrac{ \sqrt{7} (9 - \sqrt{14} ) + \sqrt{2}(9 - \sqrt{14}) }{(9) {}^{2} - \sqrt{(14} ) {}^{2} }$

$\dfrac{9 \times \sqrt{7} - \sqrt{7} \times \sqrt{14} + 9 \times \sqrt{2} - \sqrt{{14} } \times \sqrt{2} }{67}$

$\dfrac{9 \sqrt{7} - \sqrt{98} + 9 \sqrt{2} - \sqrt{28} }{67}$

HENCE DENOMIANTOR RATIONALISED

Used formula :-

(a + b) (a-b) = a²-b² for Rationalising denominator